Question

A solution containing $4g$ of polyvinyl chloride polymer in one litre of dioxane was found to have an osmotic pressure of $4.1\times 10^{-4}atm$ at $27^{\circ }C$. The approximate molecular weight of the polymer is

• A. $1500$
• B. $10,000$
• C. $2.4\times 10^5$
• D. $2\times 10^{12}$

Answer 1

Answer: (C)

Given, weight of $PVC,w=4g$
Volume of solution, $V=1L$
Osmotic pressure, $\pi =4.2\times 10^{-4}$
Temperature, $T=27^{\circ }C=27+273=300K$
$\Rightarrow \pi V=nRT$ or $\pi V=\frac{w}{M}RT$
( $M=$ molecular weight)
$4.1\times 10^{-4}\times 1=\frac{4}{M}\times 0.0821\times 300$
$M=\frac{4\times 0.0821\times 300}{4\times 10^{-4}\times 1}$
$\therefore M=2.4\times 10^5$